How do you make a cluster of cubes explode?
Add Active Rigid Body Physics to your cubes.
(I created the cubes with 3 array modifiers applied, then separated By Loose Parts, and finally moved the origins to the geometry.)
Add a force field in the middle of the stack of the cubes.
Increase the strength of the force field.
Press play or AltA and watch the explosion.


Quick gif showing the whole process.


Final result